Problem: Simplify the following expression: $ y = \dfrac{t + 7}{9t} - \dfrac{-3}{8} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{8}{8}$ $ \dfrac{t + 7}{9t} \times \dfrac{8}{8} = \dfrac{8t + 56}{72t} $ Multiply the second expression by $\dfrac{9t}{9t}$ $ \dfrac{-3}{8} \times \dfrac{9t}{9t} = \dfrac{-27t}{72t} $ Therefore $ y = \dfrac{8t + 56}{72t} - \dfrac{-27t}{72t} $ Now the expressions have the same denominator we can simply subtract the numerators: $y = \dfrac{8t + 56 + 27t }{72t} $ Distribute the negative sign: $y = \dfrac{8t + 56 + 27t}{72t}$ $y = \dfrac{35t + 56}{72t}$